The interplay of the different mechanisms together with the implications of the \(Z_{\mathcal {N}}\)  reduced-mass axion
for axion DM searches is studied in detail in [1]}, including the experimental
prospects to probe its coupling to photons,
nucleons, electrons and the nEDM operator. As an example the bounds and projections of the \(Z_{\mathcal {N}}\)  axion assuming it accounts for all the DM abundance are depicted in Fig. (REF ) for the coupling to photons and to gluons (i.e. \(1/f_a\) ).
The purple band in Fig. (REF ) encompasses the region where the prediction of the \(Z_{\mathcal {N}}\)  axion relic density within the different regimes of the trapped misalignment can account for the entire DM abundance.
As a wonderful byproduct of the lower-than-usual \(f_a\)  values
allowed in the \(Z_{\mathcal {N}}\) 
axion paradigm to solve the strong CP problem,
all axion-SM couplings are equally enhanced for a given \(m_a\) . This increases the testability of the theory in current and future experiments, see Fig. (REF ). It follows that the \(Z_{\mathcal {N}}\)  paradigm is –to our knowledge– the only true axion theory that could explain a positive signal in CASPEr-Electric phase I and in a large region of the parameter space in phase II.
Moreover, the \(Z_{\mathcal {N}}\)  axion scenario includes –to our knowledge– the first technically natural axion model of fuzzy DM that can also solve the strong CP problem.
